We numerically demonstrate the use of waveguide dispersion to shift the zero-dispersion wavelength of an As2S3 waveguide to telecom wavelengths. The device implications for parametric gain and wavelength-conversion via four-wave mixing are investigated, giving an operating bandwidth of 550 nm. We also show that the photosensitivity of chalcogenide can be used for post-fabrication tuning of waveguide dispersion characteristics.
©2007 Optical Society of America
As telecommunication bit-rates continue to grow, all-optical signal processing will become critical. Amongst these, phase-matched processes such as four-wave mixing (FWM) allow for a variety of applications, including broadband amplification, wavelength conversion, 2R and 3R regeneration and optical phase conjugation. These processes require careful dispersion control, which can be realized by engineering the dispersion in strongly confining waveguides.
It has been shown in silicon nanowires that waveguide dispersion can compensate for material dispersion and result in a zero-dispersion wavelength (ZDWL) near 1550 nm [1–3]. However, free carrier absorption (FCA) and high two-photon absorption (TPA) limit the efficiency of silicon for nonlinear processes, including FWM [1, 2]. In contrast, chalcogenide glasses such as As2S3 can have very low TPA and still possess a high nonlinearity comparable to that of silicon. As2S3 in bulk form also has large normal dispersion at telecom wavelengths, making FWM processes very inefficient.
In this paper, we propose an As2S3 waveguide design with dimensions slightly smaller than previously fabricated waveguides , which has a ZDWL at 1556 nm and low third-order dispersion. We simulate FWM in this waveguide with a device length of 10 cm and a pump intensity of 0.6 GW/cm2, and show broadband signal amplification and wavelength conversion with a peak efficiency greater than 39 dB and a 550 nm operating bandwidth with >12 dB of gain. The As2S3 waveguide design shows higher amplification and greater operating bandwidth than a recently published silicon-based design which suffers from higher TPA and third-order dispersion .
In Section 2, the results of investigations into dispersion engineering As2S3 waveguides are presented. In Section 3, we look at the performance of this engineered waveguide design for broadband amplification and wavelength conversion via FWM. Section 4 compares this performance to that of a recently published silicon waveguide design. In Section 5, the photosensitivity of chalcogenide is used to alter the waveguide dispersion characteristics. Finally, the conclusions are presented in Section 6.
2. Dispersion engineering
As2S3 exhibits strong normal dispersion at telecom wavelengths; at 1550 nm it has a group-velocity dispersion (GVD) of β2=0.45 ps2/m. For efficient FWM the pump must operate at or near zero GVD, so the ZDWL must be shifted down to the C-band region for telecoms applications. Because As2S3 waveguides are strongly confining (refractive index, n~2.38), waveguide dispersion can be used to offset the material dispersion and result in zero GVD near 1550 nm. This has been demonstrated in dispersion-shifted silica fibers, photonic crystal fibers and most recently in silicon-on-insulator (SOI) channel waveguides [1–3].
Figure 1 shows the structure of the simulated As2S3 ridge waveguide. The As2S3 is deposited onto a silica (SiO2) substrate and a polymer cladding is added after etching the waveguide. For this investigation, the etch depth is kept at 50% and the aspect ratio (height:width) is kept at 1:2 in order to reduce the losses due to sidewall roughness. Using FemSIMTM, a commercial software package from RSoft Design Group, the mode profiles and effective refractive indices were calculated over a wide wavelength range. All material refractive index data used was measured by Dr S. Madden at the Australian National University .
The resulting GVD curves of the quasi-TE mode (predominantly Ex) are shown in Fig. 2(a) for varying cross sectional areas. The effects of waveguide dispersion are clearly seen when comparing the material dispersion to the GVD of the waveguides, but it is not possible to obtain zero GVD near 1550 nm for the quasi-TE mode. Although reducing the cross sectional area to 2 µm2 lowered the normal dispersion to 0.24 ps2/m, further area reduction reversed the trend and increased the amount of normal dispersion. In fact, this is specific to the chosen geometry and can be overcome if a deeper etch is used; however this may result in higher propagation losses.
Figure 2(b) shows the GVD curves for the same cross sectional areas used previously, but for the quasi-TM mode (predominantly Ey). Although similar, these results provide a ZDWL very near 1550 nm. A 2 µm2 waveguide (1×2 µm) with a 50% etch depth has a ZDWL of 1556 nm, a low third-order dispersion, β3, of 1.26×10-3 ps3/m, and an effective mode area of 1.3 µm2.
3. Broadband amplification and wavelength conversion
FWM is a nonlinear phase-matched process resulting from the near-instantaneous third-order susceptibility, χ(3) : in nondegenerate FWM, two pump photons at frequency ωp are converted to a signal photon at ωs and an idler photon at ωi such that 2ωp=ωs+ωi. This can result in amplification of a signal wave as well as the creation of an idler wave. A bandpass filter placed at ωs results in amplification of an input signal whereas a bandpass filter placed at ωi results in wavelength conversion of the signal. However the efficiency depends on how well the phase-matching conditions are met:
Using the dispersion characteristics of the 2 µm2 design for the quasi-TM mode, the performance of the dispersion engineered As2S3 waveguide can be calculated using the split-step Fourier method. The results are shown in Fig. 3 for a pump intensity of 0.6 GW/cm2 (7.6 W), which is below the photodarkening threshold of >1 GB/cm2 , a waveguide length of 10 cm and a propagation loss, α, of 0.25 dB/cm. This attenuation is typical for current waveguides  and is expected to be reduced with improved fabrication. The peak power of the input signal is 1 nW to avoid pump depletion, and the results follow trends similar to analytic solutions , although they do include linear and nonlinear loss.
The amplification and wavelength conversion bandwidth is shown to be very broad, with a 550 nm bandwidth of >12 dB gain and a maximum gain of 39 dB. A two-pump configuration can be implemented to increase the gain of the entire bandwidth close to the maximum gain . The effects of detuning the pump from the ZDWL are also shown in Fig. 3. While a small amount of anomalous dispersion greatly reduces the bandwidth of the device it does not affect its peak gain. A small amount of normal dispersion, on the other hand, greatly reduces both the bandwidth and the peak gain, although FWM still occurs at small wavelength offsets and has, in fact, been used recently for demultiplexing 160 Gb/s PRBS to 10 Gb/s .
4. Comparison to silicon
Since many papers have been published on dispersion engineering and FWM in silicon waveguides, it is useful to compare the efficiency of our As2S3 waveguide design to a recently published silicon design . Table 1 compares the silicon parameters to those of As2S3. All silicon parameters were taken from , other than the two-photon absorption coefficient, α2, which has been taken from a more recent paper  which supersedes the reference (published by the same authors) used in . It should be noted that measurements of the nonlinear index coefficient, n2, vary from 3~6×10-18 m2/W; the highest value was used in this simulation . FCA was ignored since it was assumed the device was pumped using pulses shorter than the free-carrier lifetime.
Figure 4 compares the signal gain of the dispersion-engineered silicon and As2S3 devices, both 3 cm in length and with a pump intensity of 0.6 GW/cm2. Although the n2 of silicon is twice that of As2S3 in this simulation, its higher TPA reduces its maximum signal gain to approximately the same level of the As2S3 device. The effect of TPA becomes more prevalent for longer length devices or when higher pump intensities are used, as shown in Fig. 5, ultimately limiting the amount of gain possible with silicon. In contrast, As2S3 has very low TPA  so longer devices can be used to achieve higher signal gain.
Figure 4 also demonstrates the increased bandwidth available to the As2S3 device. This is due to its third-order dispersion (β3) being one third that of the silicon device, although this is may also be influenced not only by the material but the waveguide geometry as well. Further reduction of the cross sectional area causes a return normal dispersion, leading to a second design with a ZDWL near 1550 nm for both silicon  and As2S3 waveguides. The 1 µm2 design in Fig. 2(b) has a second ZDWL just past 1800 nm which can be moved closer to 1550 nm by going to a smaller area. However for this second silicon design, β3 is much greater than for the design used above, so this will not result in a broader bandwidth. In contrast, it is possible for an As2S3 device to have both β2 and β3 very near zero, as in Fig. 6.
5. Post-fabrication tuning of dispersion characteristics
In addition to its high nonlinearity, chalcogenide glass also exhibits photosensitivity. Intense green light has been used for writing many types of gratings into As2S3 planar waveguides, such as Bragg gratings [13, 14], long period gratings  and sampled Bragg gratings . Additionally, a uniform exposure of red light has been used for post-fabrication tuning of the resonant coupling wavelength in two-dimensional Ge33As12Se55 chalcogenide photonic crystal waveguides  and can be used for creating high-Q cavities in the same waveguides . This same method can be used to tune the ZDWL of a chalcogenide waveguide.
A uniform exposure to green light can increase the material refractive index of As2S3 by as much as 1% , effectively increasing the amount of waveguide dispersion. Figure 6 shows the effect this would have on the dispersive characteristics of two As2S3 waveguide designs, both with a 1:2 aspect ratio and 50% etch depth. A 2 µm2 waveguide can have its GVD at 1556 nm decreased by 0.0045 ps2/m, allowing for fine-tuning of the GVD at a particular wavelength or shifting the ZDWL within a 4.3 nm range. However, smaller sub-micron waveguides are much more sensitive to variations in height and width. Figure 6 also shows that a 0.85 µm2 waveguide can be tuned from a single ZDWL (with both β2 and β3 equal to zero) to having two ZDWLs as much as 230 nm apart. This ability to tune a waveguide’s dispersive characteristics after fabrication can compensate for variations which may occur during fabrication (particularly useful for smaller, more sensitive designs), as well as allowing a single waveguide design to exhibit a variety of dispersive properties.
In this paper, we presented an As2S3 waveguide design exhibiting a ZDWL within telecom wavelengths. The potential of this design was demonstrated for a 10 cm device, showing broadband amplification and wavelength conversion efficiencies of up to 39 dB over a 500 nm bandwidth at an intensity of 0.6 GW/cm2. This was compared to recent numerical results reported on a similar silicon-based device, showing that As2S3 has the potential to out-perform silicon because its device length is not limited by high TPA. The photosensitivity of chalcogenide was shown to allow significant post-fabrication tuning of sub-micron waveguide dispersion characteristics.
We thank S. Madden (ANU, Canberra, Australia) for providing us with the chalcogenide refractive index data and D. J. Moss (INRS, Montreal, Canada) for pointing out the possibility for post-tuning in chalcogenide structures.
This work was produced with the assistance of the Australian Research Council (ARC). The Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS) is an ARC Centre of Excellence.
References and links
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